Short Ballistic Josephson Coupling in Planar Graphene Junctions with Inhomogeneous Carrier Doping

We report on short ballistic (SB) Josephson coupling in junctions embedded in a planar heterostructure of graphene. Ballistic Josephson coupling is confirmed by the Fabry-Perot-type interference of the junction critical current $I_c$. An exceptionally large $I_cR_N$ product close to $2\Delta_0/e$ ($R_N$; normal-state junction resistance, $\Delta_0$ ; zero-temperature superconducting energy gap) is an indication of SB strong Josephson coupling. $I_c$ shows a temperature dependence inconsistent with the conventional short-junction-like behavior; $I_c(T)$ curves deviate systematically from the standard Kulik-Omel'yanchuk prediction. We argue that this feature stems from the planar nature of graphene junction, which is susceptible to the effects of inhomogeneous carrier doping as well in graphene near the superconducting contacts.